# STAT 5302 Assignment 3

A Corn Yield Experiment

By around 5000 bc the indigenous peoples of southern Mexico first domesticated a wild variety of corn. The earliest corn plants bore only a few kernels on each stalk. By selectively breeding these plants over thousands of years, Native Americans developed a variety of types of domesticated corn, or maize, which bore large cobs holding hundreds of kernels. In the late 1800s scientists worked on the development of hybrid corn. This research led to better varieties of corn and higher yields. An Iowan named Henry Wallace developed an early variety of hybrid corn based upon his own scientific research. The number of farmers using hybrid corn increased throughout the 20th century, and as more farmers used hybrid corn, more corn was produced. In 1933 the average yield was 33 bushels per acres. In 1997 the yield had increased to 127 bushels per acre.

In order to compare high-yield hybrids, researchers recorded the yields of corn, in bushels per plot, for four different varieties of corn, A, B, C, and D. In a controlled greenhouse experiment, the researchers randomly assigned each variety to eight of 32 plots available for the study. The yields are listed here:

 A B C D 2.5 3.6 4.3 2.8 3.6 3.9 4.4 2.9 2.8 4.1 4.5 3.1 2.7 4.3 4.1 2.4 3.1 2.9 3.5 3.2 3.4 3.5 3.4 2.5 2.9 3.8 3.2 3.6 3.5 3.7 4.6 2.7

Your task is to exhaustively analyze this data using the one-way analysis of variance (AOV) techniques of Unit 4. In the process, you should give complete answers to the following questions:

1. Are there statistical differences in average yield among the four corn varieties?
2. Is the assumption of equal population variances supported for this data? If not what did you do?
3. Do the residuals from the one-way AOV model fit suggest normality? If not what did you do?
4. Assuming you conclude that average yield is not the same for all four varieties, determine which varieties are different from which other varieties. Choose one of the many multiple comparison procedures to use. Indicate why you chose that method.

Instructions:

• Here is the data as a plain text file.
• You will notice that no guidance was given as to when to declare statistical significance i.e. what value of alpha to use. You are all big boys and girls now, so you will have to make your own decision! In any specific inference, be sure to inform the reader what value you are using, with brief reason.
• Typeset your results as a report, using the same format, template, and general instructions as for Assignment 2